Distributive semiprime rings

It is proved that a right distributive semiprime PI ring A is a left distributive ring and for each element x is an element of A there is a positive integer n such that x(n)A = Ax(n). We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive left Noetherian PI rings. We also characterize rings all of whose Pierce stalks are right chain right Artin rings.